Lie Algebras of Differential Operators and Partial Integrability

Abstract

This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.

LaTex, 25 pages. Talk presented at the IV Workshop on Differential Geometry and its Applications (Santiago de Compostela, Spain, 18--20 September 1995)

References in corpus (3)

• Lie-algebraic approach to the theory of polynomial solutions. II. Differential equations in one real and one Grassmann variables and 2x2 matrix differential equations
• Lie-algebraic approach to the theory of polynomial solutions. III. Differential equations in two real variables and general outlook
• Lie-algebraic approach to the theory of polynomial solutions. I. Ordinary differential equations and finite-difference equations in one variable

Cited by in corpus (5)

• Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra
• Interaction via reduction and nonlinear superconformal symmetry
• Exact and approximate solutions to Schroedinger's equation with decatic potentials
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Nonlinear supersymmetry as a hidden symmetry